TTP06-31 Theoretical update of Bs--Bs-bar mixing

We update the theory predictions for the mass difference Delta m_s, the width difference Delta Gamma_s and the CP asymmetry in flavour-specific decays, a_fs^s, for the Bs-Bs-bar mixing system. In particular we present a new expression for the element Gamma_{12}^s of the decay matrix, which enters the predictions of Delta Gamma_s and a_fs^s. To this end we introduce a new operator basis, which reduces the troublesome sizes of the 1/m_b and alpha_s corrections and diminishes the hadronic uncertainty in Delta Gamma_s/Delta m_s considerably. Logarithms of the charm quark mass are summed to all orders. We find Delta m_s = (49.7 =/- 9.4 ) * 10^{-4} and Delta Gamma_s =(f_{B_s}/240 MeV)^2 [(0.105 +/- 0.016) B + (0.024 +/- 0.004) B_S~' - 0.027 +/- 0.015] ps^{-1} in terms of the bag parameters B, B_S~' in the NDR scheme and the decay constant f_{B_s}. The improved result for Gamma_{12}^s also permits the extraction of the CP-violating Bs-Bs-bar mixing phase from a_fs^s with better accuracy. We show how the measurements of Delta M_s, Delta Gamma_s, a_fs^s, A_CP^mix(B_s\to J/\psi \phi) and other observables can be efficiently combined to constrain new physics. Applying our new formulae to data from the D0 experiment, we find a 2-sigma deviation of the Bs-Bs-bar mixing phase from its Standard Model value. We also briefly update the theory predictions for the Bd-Bd-bar mixing system and find Delta Gamma_d/Delta m_d = (52.6+11.5/-12.8) * 10^{-4} and a_fs^d =(-4.8 +1.0/-1.2}) *10^{-4} in the Standard Model.